Calculus • Step-by-Step

Derivative of sec(x) with Steps

Find the derivative of sec(x) step by step. Proven by writing 1/cos(x) and applying the chain rule to get sec(x)tan(x).

Problem Statement

\frac{d}{dx}[\sec(x)]

Final Result

f'(x) = \frac{\mathrm{sin}\left(x\right)}{\mathrm{cos}\left(x\right)^{2}}

Formula Required: Secant Derivative Rule

Differentiate (cos x)^(-1) using chain rule: -(cos x)^(-2) · (-sin x) = sin x / cos² x = sec x tan x.

\frac{d}{dx}[\sec(x)] = \sec(x)\tan(x)

2 Steps

Set up the differentiation problem with respect to variable $x$.

\frac{d}{dx} \left[ \mathrm{sec}\left(x\right) \right]

Apply the Power Rule to compute the derivative.

\frac{d}{dx} \left[ \mathrm{sec}\left(x\right) \right] = \frac{\mathrm{sin}\left(x\right)}{\mathrm{cos}\left(x\right)^{2}}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

The derivative of sec(x) is sec(x)tan(x).